Eccoci.

$5$-smooth numbers are numbers whose largest prime factor doesn't exceed $5$.
$5$-smooth numbers are also called Hamming numbers.
Let $S(L)$ be the sum of the numbers $n$ not exceeding $L$ such that Euler's totient function $\phi(n)$ is a Hamming number.
$S(100)=3728$.

Find $S(10^{12})$. Give your answer modulo $2^{32}$.